The members of a small town's local arts council are selling raffle tickets. The art council decides that the top three raffle ticket sellers will share a portion of the profits. The second-place seller will receive twice as much as the third-place seller. The first-place seller will receive $$ \$ 20 $$ more than the second-place seller. The profit portion they will share is $$ \$ 200 $$. 5. Draw a bar model to represent this situation.

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To represent this situation with a bar model, we can use three bars to represent the profits received by the first, second, and third-place sellers.

Let's denote:
- $$ x $$ as the amount received by the third-place seller.
- $$ 2x $$ as the amount received by the second-place seller.
- $$ 2x + 20 $$ as the amount received by the first-place seller.

The total profit shared by the top three raffle ticket sellers is $$ \$ 200 $$, so we can set up the equation:
$$ x + 2x + (2x + 20) = 200 $$

Now, we can solve this equation to find the amount received by each place seller.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x+2x+\left(2x+20\right)=200$$
- step1: Simplify:
  $$5x+20=200$$
- step2: Move the constant to the right side:
  $$5x=200-20$$
- step3: Subtract the numbers:
  $$5x=180$$
- step4: Divide both sides:
  $$\frac{5x}{5}=\frac{180}{5}$$
- step5: Divide the numbers:
  $$x=36$$
The amount received by the third-place seller is $36.

Now, we can calculate the amounts received by the second and first-place sellers:
- Second-place seller: $$ 2 \times 36 = \$72 $$
- First-place seller: $$ 2 \times 36 + 20 = \$92 $$

So, the profits shared by the top three raffle ticket sellers are:
- Third-place seller: $36
- Second-place seller: $72
- First-place seller: $92

We can now draw a bar model to represent this situation with three bars, each representing the amount received by the third, second, and first-place sellers.
The profits shared by the top three raffle ticket sellers are: - Third-place seller: $36 - Second-place seller: $72 - First-place seller: $92

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